"Other" Storage on my MacBook Air

See used and available storage space on your Mac

• Other: Contains files that don’t fall into the categories listed here. This category primarily includes files and data used by the system, such as log files, caches, VM files, and other runtime system resources. Also included are temporary files, fonts, app support files, and plug-ins. You can't manage the contents of this category. The contents are managed by macOS, and the category varies in size depending on the current state of your Mac.

There are files under your direct control and only those can be removed as you discovered. Anything else is out of yours and mine too - control

What is “Other” storage on a Mac, and how can I clean it out?

How to free up storage space on your Mac

As mentioned in earlier posting -The contents are managed by macOS, and the category varies in size depending on the current state of your Mac. It can not be altered, modified, reduced or otherwise removed by the user. I sense, because the internal drive is only 128 GB in size, there are contents it will fill up to the point the computer will stop working ? A drive of this size will require constant and prudence by you to keep from that happening. An external drive can be used to keep Photos, podcasts, Videos and music off of the internal drive except when needed.

You mentioned moving Music Library to the iCloud. It should be mentioned, storing on iCloud is not like storing on and external drive. iCloud is not a substitute for an external drive. iCloud was designed as a Conduit / way to have files on the cloud so they can be accessed by other Apple Devices you own. And, for changes made on one device is reflected on All Other deices. In reality, would is placed on the Cloud is also on the internal drive. If one deletes a music file on the internal drive - that change will also appear on the cloud. Food for thought.